Yeah, (x/y)*y = x is true whenever it's a meaningful statement. x/y has no meaning in standard mathematics when y=0. 1/0 isn't infinity or anything else in standard math, it's literally un-grammatical nonsense.

It should be true for every y that is allowed in the denominator.

That is how fractions are handled in higher math. (Either called "localization" or "ring of fractions").

It's true up to NaNs, which we can treat as bottoms.